That "recipe" is THE recipe for true Lugol's, so the Lugol's from Niles SHOULD be just fine....but THEY say it's not really Lugol's, so what's a person to assume?
Somewhere on this forum, is the recipe to make your own, and it's as simply as ordering the chemicals, getting a gram scale & a beaker/or way to measure milliters of distilled water & mixing them together.